Expressions of Market-Based Correlations Between Prices and Returns of Two Assets

ArXiv ID: 2412.13172 “View on arXiv”

Authors: Unknown

Abstract

This paper derives the expressions of correlations between prices of two assets, returns of two assets, and price-return correlations of two assets that depend on statistical moments and correlations of the current values, past values, and volumes of their market trades. The usual frequency-based expressions of correlations of time series of prices and returns describe a partial case of our model when all trade volumes and past trade values are constant. Such an assumptions are rather far from market reality, and its use results in excess losses and wrong forecasts. Traders, banks, and funds that perform multi-million market transactions or manage billion-valued portfolios should consider the impact of large trade volumes on market prices and returns. The use of the market-based correlations of prices and returns of two assets is mandatory for them. The development of macroeconomic models and market forecasts like those being created by BlackRock’s Aladdin, JP Morgan, and the U.S. Fed., is impossible without the use of market-based correlations of prices and returns of two assets.

Keywords: Market Impact, Correlation Models, Trade Volumes, Market Microstructure, Portfolio Management

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats
  • Why: The paper is heavily mathematical, deriving new correlation expressions using statistical moments, market trade equations, and detailed derivations with notation-heavy formulas. However, it lacks any empirical backtesting, data sources, or implementation details, focusing purely on theoretical model development.
  flowchart TD
    A["Research Goal<br>Determine correlation expressions<br>incorporating market impact"] --> B["Key Methodology<br>Derive statistical relationships<br>using joint distribution of trade values"]
    
    B --> C["Data Inputs<br>Current & Past Trade Prices<br>Trade Volumes for Assets A & B"]
    
    C --> D["Computational Process<br>Calculate moments & correlations<br>of price/return vectors"]
    
    D --> E["Key Findings<br>1. New correlation formulas<br>2. Classic models = special case<br>3. Essential for large portfolios"]
    
    E --> F["Outcomes<br>Improved forecasts & risk models<br>for institutional traders/banks"]